you may not have access to DNS servers
do you have an IP address through the modem connection?
can you ping a public IP address (i.e. 184.108.40.206)?
can you ping a domain name (i.e. google.com)?
If you don't have an IP, you're not connected. If you can't ping a public IP address, you are only connected to an WAN, not the internet. If you can't ping the domain name, you are only missing name resolution.
If you can't resolve names, you will need to find two DNS server addresses and manually provide them through the TCP/IP protocol configuration option of your Dial Up Networking connection object.